HeX-Sums
(Published on 13. June 2025, 09:00 by qoala)
Another exploration of 9x9 Mean-Mini-like logic using hexadecimal as the available values. I've enjoyed other puzzles using X-Sums as a clue-type for Chaos Construction regions, but there's some fun things that can be done with flexible digits.
- Hexed(0-F): Fill every row, column, & region with an identical set of 9 unique numbers, selected from 0-15 (or in hexadecimal, 0-F).
- Otherwise, normal Chaos Construction rules: Regions consist of 9 orthogonally connected cells and must be determined by the solver.
- Chaos X-Sums: Black and Red clues outside the grid indicate the sum of the first N cells in that row/column, where N is the value in the first cell seen from the direction of the clue. These N cells all belong to the same region, and the N+1th cell either belongs to a different region or is past the edge of the grid.
- Double Chaos X-Sums: In addition to acting as a normal X-Sum, Red clues outside the grid apply again starting from the N+1th cell. (The same clue indicates the sum of the M cells starting from cell N+1, where M is the value in the N+1th cell. Those M cells all belong to the same region, and the subsequent N+M+1th cell belongs to a different region, if present)
- Values in circled cells indicate how many of that cell's four edges contain a region border.
- '<' clues point to the smaller value of two cells.
Clues are in decimal, though base-16 values are provided for fun.
SudokuPad: https://sudokupad.app/zr6o3y4evb
Hexed Series:
- Hex-Proof
- HeX-Sums
Solution code: Column 8, with '-' for region borders
(9 hexadecimal characters from 0123456789ABCDEF, plus '-'s)
Comments
on 17. June 2025, 21:51 by peacherwu2
Awesome puzzle! Thanks so much!
on 17. June 2025, 08:48 by qoala
* Remove "0x##" base-16 text next to the normal clues in the LMD image.
* Remove alternate sudokupad link that only contains base-16 clues. (If you really want it, it's linked from within the sudokupad rules of the normal link).
The inclusion of base-16 clues was to satisfy what were surely joke requests on Hex-Proof. They've consistently proven confusing, so hiding them to reduce confusion.
on 16. June 2025, 09:45 by henrypijames
Does a clue like 0x1F mean that 1 and F are definitely among the 9 digits in the grid, or is there no such guarantee?
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No such guarantee. 0x1F is just hexadecimal for 31. Because on a video solve of Hex-Proof, I saw comments about the clues not being given in base 16 (strictly for the sake of it, not because it's helpful for the solve).
on 14. June 2025, 09:55 by qoala
Make it slightly clearer that the 2 sudokupad links are the same puzzle, but with different formatting for the same clues.
on 13. June 2025, 17:32 by marcmees
Very nice & challenging. A pity the 2 circles were needed to trace the last 3 regions. Thanks
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Thanks! As for the circles, when trying to finish this one, I was initially messing around with a "negative Chaos X-Sums" constraint where all valid outside clues would be given (some as '?' clues), but I couldn't get any paths that I liked to work out cleanly with the state already in the grid. Perhaps I'll work that concept into a future Chaos puzzle.
on 13. June 2025, 10:53 by marcmees
the 31 clue at the bottom of C7 is not correctly placed. Broke the puzzle immediately. -> clue should be underneath C6 according to sudokupad.
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Oops. I'm so sorry about that. That's what I get for repeatedly recreating the screenshot-formatted version of the puzzle (since a for-"print" version doesn't need the cells specifically for tracking known values) while I was editing. I guess I can at least be glad that the error immediately broke the puzzle so you didn't waste too much time on my mistake?
No. I still solve on paper but the impossibility of the clue made me check sudokupad straight away. Only wasted a page. :-)
I've fixed and re-uploaded the image.
